Question

An investor bought a number of shares of stock for $1,600. After the price dropped by $10 per share, the investor sold all but 4 of her shares for $1,120. How many shares did she originally buy?

Answer 1

Let the number of shares she bought originally be x and the price at which she bought the shares be y, then


`xy = 1,600\Rightarrow y=(1,600)/(x)` and
`(x - 4)((1,600)/(x) - 10) = 1,120`


`\Rightarrow 1,600-10x- (6,400)/(x) +40=1,120 \\ \\ \Rightarrow1,600x-10x^2-6,400+40x=1,120x \\ \\ \Rightarrow 10x^2-520x+6,400=0 \\ \\ \Rightarrow x^2-52x+640=0 \\ \\ \Rightarrow x= (52\pm √((52)^2-4(640)) )/(2) \\ \\ = (52\pm √(2,704-2,560) )/(2)=(52\pm √(144) )/(2) \\ \\ =(52+12)/(2) \ or \ (52-12)/(2) \\ \\ =32 \ or \ 20`

Therefore, the number of shares he bought originally is 20 shares of 32 shares.